The reflectivity of a target surface can be measured by irradiating the surface and measuring the fraction of the incident radiant energy that is reflected. Apparatuses and methods to perform such measurements are known, see for example the Delta and NTM500 radiation thermometers manufactured by C I Systems (P.O. Box 147, Migdal Ha'emek 10051 Israel) and the Optitherm III radiation thermometer manufactured by the Pyrometer Instrument Company (92 North Main Street, Bldg 18-D, Windsor, N.J. 08561, USA), among others. Apparatuses to perform such measurements are also described in e.g. U.S. Pat. Nos. 3,433,052, 4,708,493, 4,919,542, and 6,299,346, and in the patents referenced therein.
A schematic drawing of an exemplary prior art apparatus 100 for performing such a measurement is shown in FIGS. 1A and 1A. Apparatus 100 includes a light guide 102 that directs radiation from a radiation (e.g. light) source 104 onto a target surface 106 to form an illuminated spot 108. A fraction of the radiation reflected by the target surface is incident on a second light-guide 110, which directs this radiation to a detector 112. Frequently, there may be an optical filter (not shown) placed somewhere in the optical path between radiation source 104 and detector 112 so that the apparatus will be sensitive only to reflected radiation within a given radiation wavelength range.
For the apparatus sketched in FIGS. 1A and 1B, with a constant radiation-source intensity and constant geometry, the target surface reflectivity ρ can be determined from the relationship:V=V0+ρV1  (1)where V is the radiant intensity incident on detector 112, V0 is an offset term arising due to non-idealities in the apparatus, such as e.g. internal reflections within the apparatus, offsets in the detector, etc. and V1 is a proportionality constant that depends on the apparatus design and its positioning relative to the target surface. Examples of parameters effecting the value of the constant V1 include; the apparatus' radiation source intensity, the apparatus' radiation transmission efficiency, and the distances Ld and Le between the target surface and two probe tips 114 and 116 of light-guides 102 and 110 respectively.
Typically, equation (1) is used to determine target reflectivity after a calibration procedure that consists of two steps. First, V0 is determined by measuring the signal V when the probe views a target of zero reflectivity. This measurement is typically performed by directing the probe at a large open space, from which no reflection is returned to the probe. Next, a target calibration surface with a known reflectivity ρcalibration is placed in front of the probe, at the same distance and orientation with respect to the probe at which subsequent measurements are to be taken. A signal V=Vcalibration is generated while measuring this target. This calibration step is used to calculate V1 of equation (1) as V1=(Vcalibration−V0)/ρcalibration. Once V1 is known, equation (1) can be rearranged into a form which can be used to determine the reflectivity of all subsequently measured surfaces:
                    ρ        =                              ρ            calibration                    ⁢                                    V              -                              V                0                                                                    V                calibration                            -                              V                0                                                                        (        2        )            
Note that typically the incident radiation source is modulated, in which case the measured signal V is the amplitude of the fluctuation in reflected intensity, rather than an absolute intensity measurement. This allows the reflectivity measurement to be insensitive to the presence of reflected radiation from other interfering radiation sources and from the target's self-emission.
The existing reflectivity measurement apparatuses and methods suffer from the disadvantage that the reflected signal V is a strong function of the probe-to-target distance. Hence, significant errors in the measured reflectivity value can occur if the target surface moves relative to the position at which the calibration target was placed. The sensitivity of the measurement to variations in the probe-to-target distance is illustrated by a simple example, explained with reference to FIG. 1B. Consider a probe 102 of the general type shown in FIG. 1B, which emits from its probe-tip 114 a beam of radiation with uniform intensity within a cone-section 118 of apex angle 2θ. Consider the case where the emitted beam is incident on a specularly reflecting target surface 106. In this exemplary case, equation 1 can be written in the following form:
                    V        =                              V            0                    +                      ρ            ⁢                                                  ⁢            η            ⁢                                                            π                  ⁡                                      (                                          D                      /                      2                                        )                                                  2                                                              π                  ⁡                                      (                                                                  D                        /                        2                                            +                                                                        (                                                                                    L                              e                                                        +                                                          L                              d                                                                                )                                                ⁢                        tan                        ⁢                                                                                                  ⁢                        ϑ                                                              )                                                  2                                                                        (        3        )            Here D is the diameter of both the radiation source and detector light-guides, Le and Ld are the distances between each of these respective light-guides and the target surface (see FIG. 1A), and η is a proportionality constant that accounts for the intensity emitted by the apparatus' radiation source, the transmission efficiency of the apparatus optics, etc. The ratio in the second term in equation (3) is the ratio of the cross-sectional area of collecting light-guide 110 divided by a cross-sectional area 120 of the reflected beam as it intersects this light-guide. Since the beam has uniform intensity within the cone-section in this example, this ratio represents the fraction of the total reflected power which is collected by the probe. Solving equation (3) for the reflectivity ρ, gives:
                    ρ        =                                            (                              V                -                                  V                  0                                            )                        η                    ⁢                                    (                              1                +                                  4                  ⁢                                      L                    D                                    ⁢                  tan                  ⁢                                                                          ⁢                  ϑ                                            )                        2                                              (        4        )            where we define an probe-to-target distance L to be L=(Le+Ld)/2. That is, L is the average distance between the two probe tips and the target surface. If such a probe is now used to measure a calibration target with reflectivity ρcalibration, at a calibration probe-to-target distance L=Lcalibration, then the measured signal Vcalibration will satisfy relationship (4):
                              ρ          calibration                =                                            (                                                V                  calibration                                -                                  V                  0                                            )                        η                    ⁢                                    (                              1                +                                  4                  ⁢                                                            L                      calibration                                        D                                    ⁢                  tan                  ⁢                                                                          ⁢                  ϑ                                            )                        2                                              (        5        )            Equation (5) can be substituted into (4) to eliminate η, and obtain:
                    ρ        =                              ρ            calibration                    ⁢                                    (                              V                -                                  V                  0                                            )                                      (                                                V                  calibration                                -                                  V                  0                                            )                                ⁢                                                    (                                  1                  +                                      4                    ⁢                                          L                      D                                        ⁢                    tan                    ⁢                                                                                  ⁢                    ϑ                                                  )                            2                                                      (                                  1                  +                                      4                    ⁢                                                                  L                        calibration                                            D                                        ⁢                    tan                    ⁢                                                                                  ⁢                    ϑ                                                  )                            2                                                          (        6        )            
When L=Lcalibration, equation (6) is reduced to equation (2) and an accurate reflectivity measurement is achieved using equation (2) and the procedures described previously. However, when L≠Lcalibration, an error is introduced into the measurement. The fractional error in the measured reflectivity is given by:
                                          ρ            measured                                ρ            actual                          =                                            (                              1                +                                  4                  ⁢                                                            L                      calibration                                        D                                    ⁢                  tan                  ⁢                                                                          ⁢                  ϑ                                            )                        2                                              (                              1                +                                  4                  ⁢                                      L                    D                                    ⁢                  tan                  ⁢                                                                          ⁢                  ϑ                                            )                        2                                              (        7        )            This fractional error is plotted in FIG. 2 as a function of L/D for θ=30° and Lcalibration=D. This figure shows that when the probe moves away from its nominal position by half a probe diameter (D/2) the measured reflectivity is 0.56 times its actual value, while if the probe moves half a probe diameter closer to the target compared to the nominal position, then the measured reflectivity is 2.36 times its actual value.
Note that while equations (3) to (7) are specific to the model system described in this section, the ˜1/L2 dependence of the fractional reflectivity error in equation (7) is a general feature of such measuring systems, which typically show roughly inverse quadratic dependence on probe-to-target distance, since the divergence of the radiation beam emitted by the apparatus is a two-dimensional phenomenon.
There is therefore a need for and it would be advantageous to have a reflectivity measurement probe that is insensitive to variations in the distance between the probe and the target surface.